﻿ A triangle has two of its sides along the axes, its third side touches the circle x2 + y2 – 2ax – 2ay + a2 = 0. If he locus of the circumcentre of the triangle passes through the point (38, –37) then a2 – 2a is equal to : Kaysons Education

# A Triangle Has Two Of Its Sides Along The Axes, Its Third Side Touches The Circle x2 + y2 – 2ax – 2ay + a2 = 0. If He Locus Of The Circumcentre Of The Triangle Passes Through The Point (38, –37) Then a2 – 2a is Equal To

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## Question

### Solution

Correct option is

2812

The given circle has its centre at C (aa) and its radius is a so that it touches both the axes along which lie the two sides of the triangle. Let third side be

So that A is (p, 0) and B is (0, q) (fig) and the line AB touches the given circle. Since ∠AOB is a right angle, AB is a diameter of the circumcircle of the triangle AOB. So the circumcentre P(hk) of the triangle AOB is the mid-point of AB

i.e.          2h = p, 2k = q

circle

Hence the locus of

P(hk) is a2 – 2(x + y) + 2xy = 0.

Since it passes through (38, –37)

a2 – 2a = 2 × 38 × 37 = 2812.

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